(III) The dipole moment, considered as a vector, points from the negative to the positive charge. The water molecule, Fig. 23–47, has a dipole moment p→ which can be considered as the vector sum of the two dipole moments p→_ ₁ and p→_₂ as shown. The distance between each H and the O is about 0.96 x 10⁻¹⁰ m. The lines joining the center of the O atom with each H atom make an angle of 104° as shown, and the net dipole moment has been measured to be p = 6.1 x 10⁻³⁰ C • m . (a) Determine the effective charge q on each H atom. (b) Determine the electric potential, far from the molecule, due to each dipole, p→_ ₁ and p→_₂, and show that they sum to
V = (1 / 4π∊₀) (p cos θ / r²) ,
where p is the magnitude of the net dipole moment,p→ = p→_ ₁ + p→_₂ , and V is the total potential due to both p→_ ₁ and p→_₂ . Take V = 0 at r = ∞ .
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